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Mantel test for spatial functional data

An application to infiltration curves

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Abstract

Statistics for spatial functional data is an emerging field in statistics which combines methods of spatial statistics and functional data analysis to model spatially correlated functional data. Checking for spatial autocorrelation is an important step in the statistical analysis of spatial data. Several statistics to achieve this goal have been proposed. The test based on the Mantel statistic is widely known and used in this context. This paper proposes an application of this test to the case of spatial functional data. Although we focus particularly on geostatistical functional data, that is functional data observed in a region with spatial continuity, the test proposed can also be applied with functional data which can be measured on a discrete set of areas of a region (areal functional data) by defining properly the distance between the areas. Based on two simulation studies, we show that the proposed test has a good performance. We illustrate the methodology by applying it to an agronomic data set.

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Authors and Affiliations

  1. Statistics Department, Universidad Nacional de Colombia, Bogotá, Colombia

    Ramón Giraldo

  2. Escuela Naval de Cadetes, Cartagena, Colombia

    William Caballero

  3. Agricultural Engineering Department, Universidad Nacional de Colombia, Bogotá, Colombia

    Jesús Camacho-Tamayo

Authors
  1. Ramón Giraldo
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  2. William Caballero
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  3. Jesús Camacho-Tamayo
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Correspondence to Ramón Giraldo.

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Giraldo, R., Caballero, W. & Camacho-Tamayo, J. Mantel test for spatial functional data. AStA Adv Stat Anal 102, 21–39 (2018). https://doi.org/10.1007/s10182-016-0280-1

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  • DOI: https://doi.org/10.1007/s10182-016-0280-1

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